本征函数
数学
独特性
指数稳定性
李雅普诺夫函数
李普希茨连续性
特征向量
基本再生数
应用数学
稳定性理论
理论(学习稳定性)
零(语言学)
流行病模型
数学分析
物理
非线性系统
计算机科学
社会学
人口
人口学
哲学
机器学习
量子力学
语言学
作者
Toshikazu Kuniya,Jinliang Wang
标识
DOI:10.1016/j.nonrwa.2018.03.001
摘要
In this paper, we are concerned with the global asymptotic stability of each equilibrium of an SIR epidemic model with nonlocal diffusion. Under the assumption of Lipschitz continuity of parameters, the eigenvalue problem associated with the linearized system around the disease-free equilibrium has a principal eigenvalue corresponding to a strictly positive eigenfunction. By setting the eigenfunction as the integral kernel of a Lyapunov function, we prove the global asymptotic stability of the disease-free equilibrium when the basic reproduction number R0 is less than one. We also prove the uniform persistence of the system when R0>1 by using the persistent theory for dynamical systems. Furthermore, in a special case where the dispersal rate for susceptible individuals is equal to zero, we prove the existence, uniqueness and global asymptotic stability of the endemic equilibrium when R0>1 by constructing a suitable Lyapunov function.
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